> But for safety reasons, since the software controls when the toaster pops, you decide to check at boot time that the software hasn’t been modified.

"For safety reasons" is every single claim. For safety reasons, I want to block the manufacturer's software from doing what it wants. Why do the manufacturer's safety reasons overrule my safety reasons?

> This would be a gpl3 tivoization violation even though the whole thing is open source.

Copyleft has nothing to do with open source. You haven't done everything right on the software end, because the GPL isn't about helping developers. To do things right on the software end, you should keep GPL software out of your locked down device that you are using to restrict the freedom of its users.

> Would the toaster be a better product if you could change the software? Of course.

You just said that it would be an unsafe product if you could change the software. Now you're using the "don't let the perfect be the enemy of the good" trope to pretend that you would of course support software freedom in an ideal, magical, childish, naïve dream world.

> it seems to be an extreme overreach for the FSF to use their license

People can license their software how they want. Is it an extreme overreach for Microsoft to not let you take their Windows code and do whatever they want with it? Why are you even thinking about GPL code when there's so much overreach coming from Adobe? They don't let you use their code under any circumstances!

All of your reasoning is motivated, and I would recommend that people not buy your toaster.